Sensitivity analysis of CRA based controllers in fractional order systems

This paper focuses on robust performance analysis of a closed loop fractional order system through a sensitivity approach. The characteristic ratio assignment method is selected to attain a desired closed loop transient response. Then, we compute the sensitivity of such a desired transfer function with respect to its characteristic ratio and we explore its specifications. The relation between the coefficient diagram shape and the relative stability of the closed loop system is discussed. Also, the closed loop poles variations due to the changes in the characteristic ratios are investigated. Finally, we study a pseudo second order process to verify the robust performance of the characteristic ratio assignment approach with RST control structure.

► Fractional order controller designed by the proposed CRA method.
► The tuning parameter β is a major factor in designing a robust controller.
► The closed loop system has its maximum sensitivity to the first characteristic ratios.
► The desired step response remains almost unchanged for orders greater than a constant n0.
► The dominant poles sensitivity to the first characteristic ratios is greater than the others.